How to rig a folding laptop with a hinge?
I take it that the screen will always remain at the same angle relative to the hinge? If that's the case, move the origin of the hinge to the desired pivot point and parent the screen to the hinge. Then, you can parent the hinge to the keyboard.

By doing so, moving the keyboard will move the hinge, and rotating the hinge will rotate the screen. However, you won't be able to rotate the hinge+screen by grabbing the screen in this case, that will just detach the screen. This is Rig 1 in the included blend file.

If you don't want to move the hinge's origin, you can add an Empty Axis at the pivot point. Parent the hinge and screen to the empty, and the empty to the keyboard.
In this case, the screen and hinge are controlled by the empty, and the empty, screen and hinge will be moved around if you move the keyboard. This is Rig 2.